Models of Vocal Fold Oscillation
As is the case for most scientific phenomena, vocal fold vibration was initially explained with a somewhat simple - and as we will see, incomplete - model. As more and more has become known about human phonation, subsequent models have evolved in complexity. One of the first simple explanations of vocal fold vibration relied on basic physical laws, particularly the Bernoulli effect, the same effect that describes the 'lift' on an airplane wing. Over the past few decades, scientists have increasingly had the benefit of computer systems to create complex models to mimic vocal fold oscillation.
Myoelastic Aerodynamic Theory of Phonation
The lateral movement of the vocal folds continues until the natural elasticity of the tissue takes over, and the vocal folds move back to their original, closed position. Then, the cycle begins again. Each cycle produces a single small puff of air; the sound of the human voice is nothing more than tens or hundreds of these small puffs of air being released every second and filtered by the vocal tract. Let's further examine the myoelastic-aerodynamic theory. Myo- means muscle; the vocal folds, after all, are mostly comprised of muscle tissue. The -elastic suffix serves to remind us that the vocal fold is elastic and that we have active control over its elastic properties. Aerodynamic means that the theory deals with the motion of air and other gaseous fluids, and with the forces active on bodies in motion (such as the vocal folds) in relation to such fluids. A depiction of this simple system is shown below:
A simple rectangular block represents one vocal fold. A spring is useful for portraying the tissue stiffness or restoring force in the vocal fold. Finally, we've added a damping constant to represent the viscosity (energy absorption) of the tissue. The damping constant is similar to the shock absorber on a car or a tubular damper on a screen door. So, how well does this simple model explain how the vocal folds sustain oscillation? Not well at all, researchers have found. Bernoulli forces alone cannot account for continual energy conversion from airstream to tissue. Soon, oscillation would damp out.
The One-Mass Model
A crucial component must be added to our simple model. An acoustic tube (to represent the vocal tract) is now attached to our model. Why is the acoustic tube needed? For the vocal folds to sustain oscillation, we know there must be a negative pressure within the glottis. But, pressure from the lungs cannot be negative; it is always positive. So, how does the air pressure at the level of the glottis become negative? Make a mental image of the the air from the lungs moving uni-directionally upward. When the glottis is closing, the airflow begins to decrease, but the air that is above the glottis does not "know" this, so it continues to move with its same speed (because of inertia). This creates a region just above the vocal folds where the air pressure decreases, because air is not coming from the bottom through the glottis as fast as it is leaving above. When the vocal folds are opening, fluid pressure against the walls is greater than when the vocal folds are close together. Thus, it is the asymmetry of driving force (air) that sustains oscillation.
The Three-Mass Model
So, let's continue building our model. In order to model the shape of the vocal folds more accurately, we add two small masses (depicted as m1 and m2), one on top of the other, to represent the cover of the vocal fold. A large mass (depicted as m) represents the thyroarytenoid muscle. Although independent of one another in movement, all three masses are connected by springs and damping constants. Here is how the model looks and moves now:
Note that at some points in the cycle, the bottom of the vocal folds are farther apart than the upper part of the folds. We call this a convergent shape because the airflow is converging. On the other hand, the airflow diverges when the lowermost parts of the vocal folds are closer together; this is a divergent glottal shape. Average air pressures within the glottis tend to be larger in the convergent glottal configuration than in the divergent shape, resulting in the asymmetry of air pressures needed to sustain oscillation.
As technical capabilities in computer software and hardware increase and as improved imaging techniques allow researchers to study vocal folds in motion, models are increasingly becoming more realistic. Dr. Ingo Titze and his colleagues at The University of Iowa routinely use 16-mass models in their studies.